Cockroaches are insects of the order Blattodea, which also includes termites.
Even for main cataclysms like dropping a head, cockroaches don’t bleed very a whole lot. Unlike humans, they have an open circulatory system: A device for distributing blood thru their bodies that doesn’t depend on a closed network of arteries and veins. Their blood doesn’t pump below stress like ours, but just kind of sloshes around, making its manner into the cockroach’s tissues.
The super thing about this system, in case you’re someday going to be headless is that once a chief wound happens, blood doesn’t unexpectedly get pressured out. For a cockroach that loses its head, the blood simply clots on the neck. The cockroach could have a nasty scab for sure (in which its head was), but it won’t die from lack of blood.
Unlike people, cockroaches don’t breath via a nose or their
mouth. Instead they breathe through small holes of their bodies called
spiracles that don’t need a mind to direct them. No nostril, no mouth, and no
need for a mind to adjust your respiratory means that you can breathe all you
want to without a head.
But it is going to die from being unable to eat. And
properly before that, it’s going to die from thirst. A headless cockroach has
no mouth to drink with and could be useless from dehydration in less than a
week. Which brings the total day be counted from the moment it loses its head
to the moment it loses its existence to somewhere round 7 days or much less.
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